Does the panasonic kx-t7330 telephone system have a messaging serivice?

It all depends on what you mean by "messaging service." A 7330 instrument is just a phone that is forward and backward compatible with about 18 different Panasonic phone systems.
Each phone has the ability to light a MESSAGE button and give limited visual information to an inside caller, but it requires additional hardware to have a VOICE MAIL system. In the TA-624 which was the common system available when the 7330's were introduced, the only "system" voice mail was the TVS (in the U.S.) external voice mail box.

I hope this answers your question. You can view the features of the TA-624 here. http://www.public.carl.airpost.net/Pana/TA-624/624user.pdf

Carl